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A woman leaves for work between 8 A.M and 8:30 A.M and takes between 40 and 50 minutes to get there. Let the random variable X denote the time of her departure, and the random variable Y the travel time. Assuming that these random variables are independent and uniformly distributed , find the probability that the woman reaches before 9 A.M.

Well I tried in these way, X ~ U ( 0, 1/2 ) and Y ~ U ( 4/6 , 5/6 ) Thus I tried finding P( X+ Y < 1) but it isn't coming as desired. Please help.

Soumajit Das
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  • Consider the rectangle $A=[0,1]\times[4/6;5/6]$ on the plane and find the area ${(x,y)\in A,:,x+y<1}$. – NCh Nov 28 '17 at 23:35
  • Well mate, I can't do it. Please help me. I need a proper solution so that I can understand how to do it. – Soumajit Das Nov 29 '17 at 05:31
  • see https://math.stackexchange.com/questions/1805659/meeting-probability-of-two-bankers-uniform-distribution-puzzle?rq=1 – cgiovanardi Jan 12 '18 at 10:58

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